5 Minutes to Marriage by Carla Cassidy

By Carla Cassidy

Jack Cortland had crashed and burned in the course of his rock 'n' roll heyday. even if the good-looking loner had sworn off love, he was once single-handedly elevating his motherless sons at the relations ranch. yet hurricane clouds collected while the boys' tyrannical granddaddy alluded to eerie curses and hinted at a bad custody conflict. Out of his point, Jack employed a stunning nanny to teach him the ropes... and wound up lawfully wed!

Nanny extraordinaire Marisa Perez had reliable purposes for operating off to Vegas with Jack, yet harbored fears that possibility could darken their doorstep. but regardless of the approaching doom, Marisa couldn't face up to the smokin' scorching cowboy whose gunmetal-gray eyes captivated her heart.

And then the prophecy got here true....

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F IFRA⇒ F NBU: With the abbreviations a = −(1/x) ln F¯ (x) and b = −(1/y) ln F¯ (y) we obtain from the IFRA property for positive x, y that −(1/(x + y)) ln F¯ (x + y) ≥ a ∨ b = max{a, b} and − ln F¯ (x + y) ≥ (a ∨ b)(x + y) ≥ ax + by = − ln F¯ (x) − ln F¯ (y). But this is the NBU property F¯ (x + y) ≤ F¯ (x)F¯ (y). F NBU⇒ F NBUE: This inequality follows by integrating the NBU inequality ∞ F¯ (t)µ(t) = 0 F¯ (x + t)dx ≤ F¯ (t) ∞ F¯ (x)dx = F¯ (t)µ, 0 which completes the proof. Examples can be constructed which show that none of the above implications can be reversed.

The idea of this inequality is to give a bound on the reliability of the system at time t only based on h and µi and the knowledge that the Fi are of IFR type. , µn }. These few examples given here indicate how aging properties lead to bounds on the reliability or survival probability of a single component and how these affect the lifetime of a system comprising independent components. Bibliographic Notes. The basic reliability theory of complex systems was developed in the 1960s and 1970s, and is to large extent covered by the two books of Barlow and Proschan [33] and [34].

By defining the components in a suitable way, it is often possible to preclude dependency. For example, common mode failures that are caused by a common external cause can be identified and separated out so that the components can be considered as independent components. Another useful method for “elimination” of dependency is to redefine components. For example, instead of including a parallel structure of dependent components in the system, this structure could be represented by one component. Of course, this does not remove the dependency, but it moves it to a lower level of the analysis.

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